For the determination of the traffic lane width different techniques can be used - either the direct way by full or model scale manoeuvring tests or the indirect method using mathematical simulation models.

　

3.1 Full Scale Tests

　

 The full scale test is the most expensive method of investigating the behaviour of ships. However, it has the great advantage that no idealized situation like a model in a towing tank is used and all additional influences are taken into account. The problem regarding this positive aspect is that it is very difficult to attribute a certain result to a particular parameter because all influencing variables are changing permanently during a full scale test. For example the water depth is never constant, environmental influences like wind and current change and the behaviour of the helmsman is dependent on numerous influences.

　

 The track of the ship in former times was recorded by photographs of the river radar in constant time intervals, which were then projected on a map of the waterway to plot the position of the ship. This was a time consuming work, which nowadays has been replaced by the application of DGPS systems. The drift angle is recorded from a gyro and all data are passed to a PC. Special programs can be used to evaluate these data and give accurate plots of the path of the vessel during the manoeuvre, see Fig. 1.

　

3.2 Free Running Model Tests

　

 In model tests the influence of any parameter can be investigated separately because it is an artificial environment where the motion of the ship is observed. Besides the relative low costs which make model tests preferable there is a significant disadvantage concerning the scale effects. Normally, the tests in a towing tank are carried out under the Froude law and corrections are applied regarding Reynolds law for the hull. When carrying out manoeuvring tests Reynolds law has not only to be kept up for the hull but also for the propeller, the rudder and also for additional control devices. This is impossible but previous considerations have indicated that the scale effects of all devices add up to nearly zero.

　

 Using a 6-degree of freedom tracking system, the ships course can be observed very easily leading to an accurate method in determining the influence slight changes of manoeuvring parameters would have in the very constant environment of the towing tank.

　

3.3 Force Measurements

　

 The effect of the control devices can be measured with force gauges, either in model or in full scale. In Fig. 8 and 9 the results of such force measurements on a pushed barge (as shown in Fig. 4 and 6) are presented. It can be seen, that the lateral forces generated by the bow rudder increase significantly with the speed, while those of the thruster decrease due to flow deflection. This favours the application of a bow rudder for the normal operation and the thruster types for manoeuvres at low speed.

　

　

 The measurement of the forces affecting the whole ship by a Planar Motion Mechanism lead to a set of hydrodynamic coefficients [1], [2], which form the basis for the calculation of ship's manoeuvres [3].

　

　

 An indirect method of determining the manoeuvring behaviour of a ship is the numerical simulation of the vessel's motion based on Newtons equations of motion.

　

4.1 Mathematical Model

　

 The external forces and moments are described in dependency on the velocities and accelerations in longitudinal, lateral and yaw motion (2).

　

　

 The knowledge of the hydrodynamic and control forces enables the calculation of the motion variables for each time step of the simulation. The hydrodynamic forces can be determined by different models as e.g. the Abkowitz [4], the modular [5], [6] or the 4-quadrant model [7]. All these models are based on hydrodynamic coefficients which are either worked out with the help of PMM-tests or calculated by empirical formulas. In the example of a modular mathematical model they are separated by their origin hull, propeller and rudder (3).

　

　

4.2 Implementation of Additional Controls

　

 By simply adding a new module "additional control" to the modular mathematical model it can be extended to the simulation of bow thruster or bow rudder supported ship manoeuvres. In the standard simulation setup as presented above, only two control variables are used: the rate of revolutions of the engine(s) n and the deflection of the rudder(s) δR.

　

 For the bow steering systems a new control variable f has to be introduced which describes either the angle of the bow rudder or the rate of revolutions of the bow thruster engine, depending on the coefficients loaded into the program and the program setup. Regarding the pushed barge EIIb shown in Fig. 4 and 6 two different numerical formula have been derived from model tests representing the different behaviour of the bow thruster (4) and the bow rudder (5) taking into consideration the speed and the setting of the additional control (the thruster is only used in lateral thrust condition here).

　

　

 These formulations have been gained by using the best fit for the given experimental data. Due to the modularity of the mathematical model and the structure of the program used, the engineer is free to set up the way, the variables are defined in their input dimensions. The variable u for the speed of the vessel is used as Froude number for this module and the control variable c is rate of revolutions for the thruster and angle in degrees for the rudder.

　

 An example for the regression of the experimental data to the numerical model is given in Fig. 10 for the lateral force of the bow thruster.

　

　

4.3 Simulation Runs

　

 For the investigation of the influence an additional control device would have on the traffic lane width an extensive series of simulation runs were carried out using the formulations for the controls described above. The mathematical model of an inland vessel coupled with an EIIb pushed barge equipped with different bow control systems was based on varying the parameters listed in table 1 below. Additional variations according to the ship's length, the draught and the position of the thrusters were made but have not been considered within this paper.